# Reduced-Order Distributed Unknown Input Observer for State Estimation and Unknown Input Reconstruction

## TL;DR

This paper introduces a new observer design that estimates system states, unknown inputs, and measurement noise in distributed systems.

## Contribution

The novel contribution is a reduced-order distributed unknown input observer that achieves asymptotic convergence for state and unknown input estimation.

## Key findings

- A reduced-order distributed observer was designed to estimate states and unknown inputs asymptotically.
- The method decouples control inputs and handles measurement noise in distributed systems.
- Simulation results demonstrate the effectiveness of the proposed approach.

## Abstract

In traditional observer designs, simultaneous state estimation, unknown input reconstruction (UIR), and measurement noise reconstruction have been fully discussed. However, in distributed observer, this remains to be investigated, and few papers deal with this problem. This paper designs a reduced-order distributed unknown input observer (DUIO) to offer the asymptotic convergent estimations of both the states, the unknown input (UI) and measurement noise (MN), for the uncertain target system with UI and each sensor node with MN. Firstly, by introducing an auxiliary output, the local system in every node is transformed into a system whose output contains no MN. Secondly, for the transformed local system, a distributed reduced-order observer produces asymptotically convergent state estimations. Thirdly, based on the interval observer and state estimation, a UIR is designed, and the UIR can estimate the real UI asymptotically. Moreover, the UIR decouples the control input. Finally, a simulation example is given to illustrate the effectiveness and advantages of the proposed method.